What is the squared root of 14400?

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Answer 1 · 2015-12-02T03:10:36

$= 120$ $=color(blue)(120$

$\sqrt{14400}$ $sqrt14400$

We prime factorise the number first (express the number as a product of primes):

$\sqrt{14400} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 5}$ $sqrt14400=sqrt(2*2*2*2*2*2*3*3*5*5)$

$= \sqrt{2^{6} \cdot 3^{2} \cdot 5^{2}}$ $=sqrt(2^6 * 3^2 * 5^2)$

$= {(2^{6} \cdot 3^{2} \cdot 5^{2})}^{\frac{1}{2}}$ $=(2^6 * 3^2 * 5^2)^(color(blue)(1/2$

$= (2^{6 \cdot \frac{1}{2}}) \cdot (3^{2 \cdot \frac{1}{2}}) \cdot (5^{2 \cdot \frac{1}{2}})$ $=(2^(6*1/2)) * (3^(2*1/2)) * (5^(2*1/2))$

$= 2^{3} \cdot 3 \cdot 5$ $=color(blue)(2^3*3*5$

$= 120$ $=color(blue)(120$